Products of Commutative Rings and Zero-Dimensionality

DOI10.2307/2154134zbMath0760.13005OpenAlexW4252908282MaRDI QIDQ4018459

Robert Gilmer, William J. Heinzer

Publication date: 16 January 1993

Full work available at URL: https://doi.org/10.2307/2154134

zbMATH Keywords

directed union of Artinian ringsimbeddability of a commutative ring into a zero-dimensional ringKrull dimension of a direct product of rings

Mathematics Subject Classification ID

Commutative Noetherian rings and modules (13E05) Ideals and multiplicative ideal theory in commutative rings (13A15) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Dimension theory, depth, related commutative rings (catenary, etc.) (13C15)

Related Items (25)

ZERO-DIMENSIONAL SUBRINGS OF A PRODUCT OF COMMUTATIVE RINGS ⋮ Imbeddability of a commutative ring in a finite-dimensional ring ⋮ Products of zero-dimensional pairs ⋮ Some topology on zero-dimensional subrings of product of rings ⋮ Noetherian-like properties and zero-dimensionality in some extensions of rings ⋮ Everywhere vanishing polynomial functions ⋮ FMR-rings in some distinguished constructions ⋮ Maximal and minimal prime ideals of incidence algebras ⋮ Ring extensions with finitely many non-Artinian intermediate rings ⋮ When is a power series ring \(n\)-root closed? ⋮ Desingularization of regular algebras ⋮ Unnamed Item ⋮ The family of residue fields of a zero-dimensional commutative ring ⋮ On the Set of Artinian Subrings of Infinite Products of Rings ⋮ Prime ideals in ultraproducts of commutative rings ⋮ ARTINIAN SUBRINGS OF PRODUCT OF ZERO-DIMENSIONAL RINGS ⋮ Zero-Dimensionality in Commutative Rings ⋮ Height theorems and unmixedness for finitely generated algebras over zero-dimensional rings ⋮ Artinian Subrings of a Commutative Ring ⋮ On the Imbedding of a Direct Product into a Zero-Dimensional Commutative Ring ⋮ On the transfer of the notion directed union of Artinian subrings ⋮ About directed unions of Artinian subrings of a Von Neumann regular ring ⋮ Surjections of unit groups and semi-inverses ⋮ The residue fields of a zero-dimensional ring ⋮ Commutative rings with periodic multiplicative semigroup

Cites Work

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• Dimension theory of commutative rings without identity
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• Integral domains with Noetherian subrings
• On polynomial rings over a Hilbert ring
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• On Prüfer domains of polynomials.
• Some Countability Conditions on Commutative Ring Extensions
• The Noetherian Property for Quotient Rings of Infinite Polynomial Rings
• Two Criteria for Dedekind Domains
• Residually Finite Rings
• Rings with Finite Norm Property

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